1. Field of the Invention
The present invention relates to a method and apparatus for determining a particle size within a given medium. More particularly, the particle size may be determined using a single wavelength to confirm a known particle size within a dispersion, or determined using two wavelengths to calculate an unknown particle size within a dispersion. Three wavelengths may be used to determine an unknown particle size within a dispersion with unknown concentration. The method and apparatus may be used for mono-dispersions and poly-dispersions.
2. Brief Description of the Related Art
As monochromatic light traverses a random, attenuating medium, the radiant intensity decays exponentially with path length and attenuation coefficient. This relationship was first formulated by Pierre Bouguer (1698-1758). Many authors also credit Lambert for deriving this relation. When the attenuation is expressed in terms of the particle concentration, the formula for exponential decay is known as Beer's Law. Beer's law was used to determine the concentration of an absorbing substance by comparing to a standard substance of known concentration. The exponential decay law has thus been called the Bouguer, Lambert, or Beer Law, or some hyphenated combination of these three, herein referred to as the Bouguer-Lambert-Beer Law, or the BLB law.
Considerable confusion exists regarding the applicability limits of the Bouguer-Lambert-Beer Law of optical transmission. The BLB law can be derived directly from conservation of energy considerations. As such, it is a heuristic law. It also can be derived, under certain simplifying assumptions, as a solution to the radiative transport equation (RTE), which is itself a heuristic formula.
Light traversing a random medium is attenuated by both scattering and absorption. It is well known that radiant intensity measured after the light traverses the medium cannot include any scattered light. For this reason, the BLB law has often been called the BLB law of optical absorption. It has been generally assumed that the BLB law is valid only when scattering is negligible. Some authors have recognized the applicability of the BLB law to optically dense media, provided the scattered light is appropriately filtered. Several articles have heretofore stated that the BLB law was an approximation, because the scattered light cannot practically be excluded.
Several methods are known for determining the mean size in a sample of particles. One method includes scanning the sample with an electron microscope, and processing the resulting image, either by hand or with image processing software, to determine the mean size of the particles within the image.
A second method, described in Absorption and scattering of light by small particles, by Bohren and Huffman, Wiley and Sons, 1983, Section 11.17, measures the extinction, i.e., optical thickness, as a function of wavelength which is compared to curves calculated from the Mie theory. This requires a spectrophotometer capable of making measurements over a large range of wavelengths, as well as a library of extinction curves, generated from the Mie theory over the same wavelength range, for many different sizes and refractive indices. The measured curve is compared to the curves in the library and the curve that best matches the data is chosen as a mean size of the particles in the sample.
The third method measures scattered intensity at a given angle, usually 90 degrees, with the incident intensity known. A lookup table is prepared for the expected measured intensity at that angle over a range of sizes at a specific refractive index ratio. The values in the table are generated from the Mie theory. The measured intensity is compared to the values in the table. The closest match corresponds to the mean size of particles in the sample.
The fourth method, described in "Determination of soot parameters by a two-angle scattering-extinction technique in an ethylene diffusion flame," by De luliis et al., Appl. Opt., vol. 37, no. 33, p. 7865, 1998, measures the extinction as in the second described method at a single wavelength. The scattering is assumed negligible and the attenuation is due only to absorption. This requires a very dilute sample and a laser wavelength for which the particles are strongly absorbing. Thus, for sampling many different types of materials, a frequency agile laser or multiple lasers is required. The absorption coefficient is proportional to the cube of the particle size. Measurement of the extinction yields the absorption, which yields the mean particle size in the sample.
A fifth method measures the Doppler shift in the scattered light. For particles suspended in fluid heterodyne detection methods are required since the frequency shift is small. This method requires a complicated setup and data analysis. The line width of the scattered spectrum is proportional to the diffusion coefficient, which is inversely proportional to the particle size.
Accordingly, there is a need in the art to provide a method and apparatus to apply the BLB law for scattering media with increased concentrations, and without the necessity of generating and comparing libraries of curves.